94 power problem

Hello,
Does any one have any idea what might be causing this problem?
I have a new starter, new alternator and a new battery...
The car runs fine for a while then the lights get dim, the radio shuts off.. battery light comes on.. then.. it dies..
I mess with the positive cable on the battery and sometimes it will start again and run.. the cable is on as tight as it goes.. it also has been cleaned well and so has the battery post..
All the connections to the starter and alternator and battery have been checked and rechecked.
Everyone that I and my sons have talked to can not figure it out.. the battery never goes dead either because, after a while someone can come and it starts right back up.
Would welcome any suggestions.

lacym099